HELPING CHILDREN STRATEGIES - Professional Learning

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HELPING CHILDREN BUILD MENTAL MATH AND COMPUTATION STRATEGIES

Book Study: Number Talks by Sherry Parrish

Grades 2 – 5 Wednesday, June 5th

Facilitated by: Christine Roberts [email protected]

Goals/Agenda

�  Welcome �  Overview �  Sample Number Talks �  Videos �  Routine

¡  Teacher’s role ¡  Student expectations

�  Supporting the Common Core State Standards �  Next Steps �  Wrap Up

Norms

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Number Talks

�  Calculate the following mentally. �  Be prepared to share strategies aloud.

8 + 6

Number Talks by Sherry Parrish

Number Talks: Video

Classroom Clip: 2.1 � Watch the video showing a Second Grade

addition Number Talk. Discuss (with your elbow partner): � What is the teacher’s role in the number talk? � What features of this video would you like to

see in your classroom?

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Why Number Talks?

The practice of number talks is one of the most powerful vehicles I know for helping students learn to

reason with numbers and make mathematically convincing arguments, for building a solid foundation for algebraic reasoning, and for teaching mathematics

as a sensemaking process. If all teachers make this shift in their practice, it would represent a profound

advancement in mathematics education.

- Ruth Parker


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What are Number Talks?

u Classroom conversations around purposefully crafted computation problems that are solved mentally.

u The problems are designed to elicit specific strategies that focus on number relationships and number theory.

u Students are given problems in either whole- or small-group settings and are expected to mentally solve them accurately, efficiently, and flexibly.

u By sharing and defending their solutions and strategies, students have the opportunity to collectively reason about numbers while building connections to key conceptual ideas in mathematics.


Rationale for Number Talks � “Our classrooms are filled with students and

adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules.”


Accuracy, Efficiency, and Flexibility

� “Accuracy denotes the ability to produce an accurate answer; efficiency refers to the ability to choose an appropriate, expedient strategy for a specific computation problem; and flexibility means the ability to use number relationships with ease in computation.”


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Focusing on the Mathematical Process, NOT Answer Getting

�  Students are asked to defend or justify their answers to prove their thinking

�  Students have a sense of shared authority in determining whether an answer is accurate

�  Teacher is not ultimate authority �  Wrong answers are used as opportunities to unearth

misconceptions �  Students investigate their thinking and learn from

mistakes �  Mistakes play an important role in learning and provide

opportunities to question and analyze thinking, bring misconceptions to forefront, and solidify understanding

Number Talks by Sherry Parrish, pages 11-12

My Favorite No

� The Teaching Channel: �  https://www.teachingchannel.org/videos/class-

warm-up-routine

The Teaching Channel, https://www.teachingchannel.org/videos/class-warm-up-routine

Number Talks: Video

Teacher Interview � Watch the video showing a Teacher Interview. Discuss (with your face partner): � How does the teacher feel about Number Talks? � How have Number Talks influenced her

classroom and her teaching?

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Number Talks Articles

� Choose one of the articles to read.

¡ Stand-Up, Hand-Up, Pair-Up

¡ Share your thoughts and questions after reading the article.

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Tulare County Office of Education

Number Talks

�  Calculate the following mentally.

1000 - 674


Classroom Clip: 3.1

As you watch the video, consider: �  What evidence in the video supports student

understanding of place value? �  How do the student’s strategies exhibit number

sense? �  Which strategies were more accessible to you: More

challenging to follow? �  How are accuracy, flexibility, and efficiency

interwoven in the students’ strategies?


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What Are Number Talks?

Key Components of Number Talks

1)  Classroom environment and community 2)  Classroom discussions 3)  The teacher’s role 4)  The role of mental math 5)  Purposeful computation problems


�  Mental math problems posed �  Students are given think time and indicate a solution

and multiple strategies �  Students share solutions and explain their thinking �  Encourages students to communicate about math �  The teacher acts as a facilitator and his/her primary

function is to question students in order to guide the discussion

Overview


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�  Daily, 5-15 minutes �  Consistent location �  Students in close proximity, seated on the floor or in

chairs �  Easy visibility for teacher and students �  Teacher records student thinking on the whiteboard

and/or chart paper �  Problem or string of problems are posed �  Students are given think time �  Teacher facilitates a conversation around the problem(s) posed that day Number Talks by Sherry Parrish

Routine

Number Talks Hand Signals

o  Teach the Hand Signals o I have an answer (Thumb up in front of chest) o I agree (“hang ten” back and forth) o I disagree (hands back and forth by ears or in front of body)


Classroom Discussions

�  Teacher writes problem on board and give students time to solve the problem mentally.

�  Once students find an answer, they are encouraged to continue finding efficient strategies while others are thinking.

�  Students indicate when they are ready with a solution by quietly raising a thumb against their chest. They indicate they have other approaches by raising another finger for each solution.


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Classroom Discussions Continued

�  The quiet form of acknowledgement allows for more student think time at the same time as challenging students that already have an answer.

�  All answers- correct and incorrect- are recorded. �  Students share strategies and justifications with

peers.


Benefits of Sharing and Discussing Computation Strategies

Students have the opportunity to: 1.  Clarify their own thinking. 2.  Consider and test other strategies to see if they are

mathematically logical. 3.  Investigate and apply mathematical relationships. 4.  Build a repertoire of efficient strategies. 5.  Make decisions about choosing efficient strategies

for specific problems.



59 + 13

Sample Number Talk


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Classroom Clip: 32

As you watch the video, consider: �  What evidence in the video supports student

understanding of place value? �  How does each strategy foster number sense and the

use of number relationships? �  Which strategies were most accessible to you? More

difficult to follow? �  Choose one of the strategies to model with the open

number line. How could this be an effective tool for your students?


Teacher and Student Roles in Number Talks

Roles and Participation

�  Teacher’s role ¡  Planning - be purposeful in

the selection of problems ¡  Facilitating ¡  Questioning ¡  Recording answers/student

thinking ¡  Accepting – accept and

record answers/explanations without confirming or denying

�  Student participation ¡  All students work to find an

answer ¡  Signal that they have an

answer and if they have multiple strategies

¡  Share and explain their thinking

¡  Defend their thinking ¡  Inquire about the thinking

of others


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The Teacher’s Role

�  Teacher's role shifts from being sole authority in giving information and confirming correct answers

�  Teacher is facilitator, questioner, listener, and learner

�  Guide students to ponder and discuss examples that build upon teacher’s purposes.

�  “How did you get your answer?” �  “By changing my question from “What answer did

you get” to “How did you solve this problem?” I was able to understand how they were making sense of mathematics.”


�  Plan problems with a purpose/goal in mind �  Pose the problem(s) for the day �  Record student responses to reflect how they were

explained (not the teacher’s interpretation) �  Practice notation to represent student thinking

accurately �  Provide the structure and procedures to facilitate the

Number Talks �  Post sample prompts to helps students structure their

explanations or questions in front of the class �  Be aware of the equal sign and use it properly

Teacher Responsibilities


Choosing Purposeful Problems

�  Craft problems that guide students to focus on mathematical relationships.

�  Teacher’s goal and purpose should determine the

numbers and operations that are chosen.

Discuss: �  How might you work together to select and plan for

number talks?


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Number Talks are a Purposeful Vehicle to:

�  Make sense of mathematics �  Develop efficient computation strategies �  Communicating mathematically �  Reasoning and proving solutions


Sample Number Talk and Video

�  Classroom Clip 5.3:

16 x 35


As you watch the Number Talk, consider:

1)  What procedures are in place that allow students to share their thinking?

2)  What opportunities exist for the teacher to informally assess student understanding?

3)  How is student communication encouraged and valued?

4)  How would you describe the teacher’s role during the number talk?


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Developing Student Strategies and Supporting all Learners

Developing Accountability with Students

1)  Ask students to use finger signals to indicate the most efficient strategy.

2)  Keep records of problems posed and the corresponding student strategies.

3)  Hold small-group number talks throughout each week. 4)  Create and post class strategy charts. 5)  Require students to solve an exit problem using the

discussed strategies. 6)  Give a periodic computation assessments to monitor

growth.


Supporting Students

�  Use this time to make informal observations and interactions.

�  Provide appropriate wait time to ensure that the majority of the students have accessed the problem.

�  Validate student thinking by accepting all answers. �  Encourage student communication throughout the

number talk.


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Developing Strategies

�  Discuss with your partner at least four different strategies to solve 28 + 29.

�  How will you teach alternate strategies to students?


28 + 29

Sample Number Talk


Classroom Clip: 3.1 Discuss: �  How does the teacher’s recording of each strategy

provide access for all students? �  Which strategies are easiest for you to understand? �  Which strategies are more challenging to follow? �  What mathematical concepts are being addressed during

the number talk. �  How did the teacher bring these ideas to the forefront for

the class?

Number Talks: Video


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Supporting English Learners

�  According to David Foster, mathematics director, founder of the Silicon Valley Mathematics Initiative for the Noyce Foundation,

“Number Talks are one of the most important routines you can implement in order for EL students to be successful in mathematics. The key is in how you record student responses.”


Come se suma?/How do we add?

�  A Number Talk in Spanish from Inside Mathematics: �  http://www.insidemathematics.org/index.php/2nd-

grade-icomo-se-suma-how-do-we-add

Inside Mathematics, insidemathematics.org

“K, Counting and Cardinality; K-5, Operations and Algebraic Thinking,” page 6, www.commoncoretools.wordpress.com

OA Progression

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8 Common Addition Strategies

1.  Counting All 2.  Counting on 3.  Doubles/Near-Doubles 4.  Making Tens 5.  Making Landmark or Friendly Numbers 6.  Compensation 7.  Breaking Each number into its Place Value 8.  Adding Up in Chunks

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Number Talks

�  Calculate the following mentally. �  Try to use multiplication strategies.

12 x 15


Multiplication and Division Strategies

� Repeated addition or skip counting

� Partial products

� Breaking factors into smaller factors

� Making a landmark or friendly number

� Doubling and halving

� Repeated subtraction or sharing/dealing out

� Multiplying up

� Partial quotients

� Proportional reasoning


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Number Talks


150÷15


Number Talks


300÷15


Number Talks Video

Classroom Clip: 5.4 Discuss: �  How did this particular sequence of problems help

students use number relationships to solve the problems?

�  What student confusions and misunderstandings surfaced with the array model?

�  How did the teacher navigate the discussion to build understanding about multiplication, division, and array model?


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Number Talks

�  Anticipate possible student strategies and how they might be recorded.

496 ÷ 8

Supporting the CCSS for Mathematics

7 = 4 + 3

4 + 3 = 3 + 5

?

?

9 = 16 - 7

16 - 7 = 7 - 16

?

?

True/False with

Justification

The Silicon Valley Mathematics Initiative

Math Assessment Collaborative

Content Student

Teacher

Learning

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2

The Silicone Valley Mathematics Project

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7 + 6 = + 5

12 + 9 = 10 + 8 +

43 + 28 = + 42

28 + 32 =27 +

The Silicone Valley Mathematics Project

NUMBER TALKS: RELATIONAL THINKING

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Mathematically proficient students:

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning


The Standards for Mathematical Practice

Mathematical Practices - Discuss

�  What are some of the ways that the Mathematical Practices Standards are demonstrated through Number Talks?

Talking Chips 1.  The teacher provides a discussion topic and think time. 2.  Any student begins the discussion, placing one of his/her chips in

the center of the table. 3.  Any student with a chip continues discussing, using his/her chip. 4.  When all chips are used, teammates each collect their chips and

continue the discussion using their talking chips (until the teacher stops the discussion).


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Guess My Rule �  Extending Number Talks

to Other Math Concepts from Inside Mathematics:

�  http://www.insidemathematics.org/index.php/5th6th-grade-guess-my-rule

Inside Mathematics, insidemathematics.org

Planning for Number Talks

�  Identify grade level standards that require the type of mathematical thinking that Number Talks Promotes.

� Write several problems with your table group for your selected standards.


Getting Started and Next Steps

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1.  Start with smaller problems to elicit thinking from multiple perspectives

2.  Be prepared to offer a strategy from a previous student

3.  It is okay to put a student strategy on the back burner

4.  As a rule, limit to 5-15 minutes 5.  Be patient with yourself and students as you

incorporate Number Talks into your regular math time

Tips for Getting Started


Next Steps

� What are your next steps in preparing Number Talks for next school year?

� What did you learn from today’s session?

� What do you still need to learn?


Resources

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commoncore.tcoe.org


�  Questions/comments �  Resources:

¡  http://mathperspectives.com/num_talks.html ¡  http://www.insidemathematics.org/index.php/classroom-

video-visits/number-talks ¡  http://sdcounts.tie.wikispaces.net/file/view/

Numbertalks.pdf ¡  http://www.sandi.net/cms/lib/CA01001235/Centricity/

Domain/101/Math%20Documents/Routines/mid_level_routinebank.pdf

Resources


¢ TCOE Instructional Services �  www.tcoe.org/ERS/CCSS

¢ TCOE Common Core Repository �  www.commoncore.tcoe.org

�  E-mail:

Christine Roberts [email protected]

Resources


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� Have a great day!

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